Global/Local iterative homogenization methods for neutron diffusion nodal theory

Abstract

The objective of this research is to develop efficient spatial homogenization methods for coarse-mesh nodal analysis of the light water reactors in which the reference solutions are not known. The methods developed are the global/local iterative procedures, including procedures based on variational principles. The nodal expansion method (NEM) with generalized equivalence theory is employed in coarse-mesh nodal analysis. The finite difference method (FDM) is used in fine-mesh local assembly calculation. To achieve fast and stable convergence in local assembly calculation, the mixed boundary condition is imposed at the assembly surface, where the surface flux is modulated. The assemblywise fundamental mode eigenfunction is used as the modulating function. Two direct methods are developed for the global/local iterative homogenization : $G_1$ and $G_2$ㆍ$G_1$ procedure is based on the rigorous definition of the flux-weighted constants (FWCs) and $G_2$ procedure preserves the reaction rate ratio. Three variational principles are also proposed for the assembly homogenization. The basic form is inferred from the Pomraning``s variational principle. Since the two variational methods, $F_0$ and $F_2$, are based on the ratio of reaction rates, these are insensitive to the amplitude of the flux and hence they are of the Lagrangian form. On the while, the other variational principle $F_1$ is based on the reaction rate and this requires a normalization due to its property that is sensitive to the amplitude of the flux. Thus the resulting form of $F_1$ becomes the Swinger type. The homogenization methods developed were applied to the LWR problems. In the PWR problems we treated, there is no strong need for a global/local iterative homogenization procedure, since the heterogeneity between the fuel assemblies is relatively weak. Using the assembly discontinuity factor(ADF), the nodal analysis was improved with reasonable accuracy, while no significant improvement was observed...